A leaked general election script for Labour MPs reveals that the party will direct its campaign focus to core issues including schools, social care and the NHS, rather than immigration, defence and Brexit.

The document passed to the Guardian reveals that the party’s dominant line of attack will be that the Conservatives are for “the privileged few” and that Labour will be “for the many, not the few”.

Immigration – one of the key issues for the party in its northern heartlands, where constituents voted in large numbers to leave the EU – is not mentioned. MPs are told to emphasise that the election “is not a rerun of the EU referendum” and that the party only objects to the Tories’ “reckless approach to Brexit”.

In a speech on Tuesday, the shadow Brexit secretary, Keir Starmer, said Labour would not make controlling immigration its priority as the UK leaves the EU.

The script, a two-page document that mentions Jeremy Corbyn’s name only once, says the election should be seen as a chance for “a fresh start”. The position will be that the Conservatives have a “reckless approach to Brexit [which] threatens to put millions of jobs at risk”.

Labour will promise to increase spending on infrastructure and public services, the script says. Among the key pledges are a £10-an-hour living wage, a national investment bank to create £500bn to fund capital projects and infrastructure, and a guarantee on the triple lock for pensions.

The script also invites MPs to say a Labour government “will always give the NHS the money it needs”.

On education, MPs are to say Labour will focus on “reducing class sizes and driving up teaching standards” while the Tories “only look backwards to bring back selection, which will benefit only the lucky few”.

Spending pledges include free school meals for primary school pupils, reintroduction of the education maintenance allowance, and maintenance grants for students from low-income and middle-income backgrounds.

The script says a Labour government would build more than 1m homes in five years, with at least half of these in the social rent sector.

The script makes little or no mention of topics where the Conservatives are traditionally strong, including defence and the armed forces, and crime. Labour MPs are handed an attack line, however, which says the Tories “broke their promise to protect the police” and that “more than 20,000 police officers and 6,000 police community support jobs have been cut since 2010”.

The party is due to finish drawing up its list of candidates for all seats by 5 May, following a meeting of the national executive committee on 3 May, the Guardian understands.

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Newcomers could battle to replace retiring Labour MPs with relatively safe seats, including Jim Dowd, in Lewisham West and Penge, and Alan Johnson, in Hull West. Several Corbyn advisers are thought to be vying for Johnson’s seat, including his former spokesman Sam Tarry and his speechwriter, David Prescott.

Karie Murphy, head of Corbyn’s office, and Katy Clark, Corbyn’s political secretary and the former MP for North Ayrshire and Arran, are also thought to have put their names forward as candidates for seats. The trade unionist Stephanie Peacock, former partner of Labour’s deputy leader, Tom Watson, will compete for the Barnsley East seat vacated by Michael Dugher.

In Lewisham, there is expected to be a close contest between Ellie Reeves – a former Labour NEC member, sister of Rachel Reeves, and spouse of the MP John Cryer – and Christian Wolmar, a former Richmond Park candidate and transport campaigner. Ibrahim Dogus, founder of the British Kebab Awards, has also put his name forward for that south London seat.

The party’s manifesto launch has been pencilled in for 15 May, drafted by Corbyn’s adviser Andrew Fisher, previously a Public and Commercial Services union official. It will pull together ideas agreed by the party’s executive and shadow cabinet at a critical “clause V” meeting on 11 May.

Corbyn met the cabinet secretary, Sir Jeremy Heywood, on Tuesday to lay out Labour’s plans for government, as Whitehall gears up for the election.

Notwithstanding the Conservatives’ commanding lead in the polls, it is part of the civil service’s role during an election campaign to prepare for the possibility of a change of administration.

The meeting was attended by key Labour strategists including Corbyn’s director of communications and strategy, Seumas Milne. The Labour delegation presented Heywood with briefing papers on the party’s policies.

A spokesman for Corbyn said: “The meeting, with the support of staff and colleagues, was detailed and productive and will now be followed by departmental discussions. Jeremy would like to put on record his appreciation of the professionalism and commitment of the cabinet secretary and his civil service colleagues.”

Shadow cabinet ministers will now hold one-to-one meetings with the permanent secretaries of the relevant departments in the coming weeks, though some are said to be concerned about letting civil servants know too much about the party’s manifesto before it is launched in mid-May.